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We investigate the problem of message transmission and the problem of commonrandomness (CR) generation over single-user multiple-input multiple-output(MIMO) slow fading channels with average input power constraint, additive whiteGaussian noise (AWGN), arbitrary state distribution and with complete channelstate information available at the receiver side (CSIR). First, we derive alower and an upper bound on the outage transmission capacity of MIMO slowfading channels for arbitrary state distribution and show that the boundscoincide except possibly at the points of discontinuity of the outagetransmission capacity, of which there are, at most, countably many. To provethe lower bound on the outage transmission capacity, we also establish thecapacity of a specific compound MIMO Gaussian channel. Second, we define theoutage CR capacity for a two-source model with unidirectional communicationover a MIMO slow fading channel with arbitrary state distribution and establisha lower and an upper bound on it using our bounds on the outage transmissioncapacity of the MIMO slow fading channel.

Message Transmission and Common Randomness Generation over MIMO Slow Fading Channels with Arbitrary Channel State Distribution